Snakes and electric fences: An innovative approach of teaching curve sketching in undergraduate Mathematics

In the study of Algebra and Calculus, curve sketching is always very interesting for both the teacher and the learner. This paper describes an innovative way of teaching curve sketching to first year undergraduate students by using the analogy of snakes and electric fences. A snake represents a continuous curve and an electric fence marks a forbidden zone or an asymptote. Given a mathematical function, y = f(x), the learner will learn to identify the zone(s) in which the snake is allowed to wander, the forbidden zones that cannot be crossed by the snake, the positions for its ends (called head and tail for convenience), possible crossings on the x-axis and y-axis by the snake, and any other `twists and turns' of its body that will lead to a clear trace of its body. The complete trace of the snake's body will then be the curve for the mathematical function y = f(x). This approach will certainly spice up the learning process and strengthen the conceptual understanding of the various mathematical aspects in curve sketching. Mastering the skills of curve sketching by this approach will also give the learner some insights on finding real solutions to polynomial equations.